A train leaves the station at 8 a.m. and averages 40 miles per hour another train leaves the same station one hour later and averages 50 miles per hour traveling in the same direction on a parallel track at what time will the second train catch up with the first train how many miles would each train have traveled by that time

Question

A train leaves the station at 8 a.m. and averages 40 miles per hour another train leaves the same station one hour later and averages 50 miles per hour traveling in the same direction on a parallel track at what time will the second train catch up with the first train how many miles would each train have traveled by that time

Answer 1

Time taken by the slower train ---- t hrs

time taken by faster train --------- t - 1 hrs

distance gone by slower train = 40t miles
distance gone by faster train = 50(t-1) miles

But, when they pass each other, each will have covered the same distance, so

50(t-1) = 40t
50t - 50 = 40t
10t = 50
t = 5

Since the slower train left at 8:00 am and it took 5 hours for them to meet, they met at 1:00 pm

The distance they both went is 200 miles

Answer 2

To find out when the second train will catch up with the first train, we need to calculate the time it takes for the second train to cover the same distance as the first train.

Let's assume that it takes t hours for the second train to catch up with the first train.

Now, let's calculate the distance traveled by each train by that time.

Since the first train has been traveling for t hours when the second train catches up, it would have covered a distance of 40 * t miles.

The second train leaves one hour later than the first train, so it has been traveling for t-1 hours when it catches up. At an average speed of 50 miles per hour, it would have covered a distance of 50 * (t-1) miles.

Since both trains have covered the same distance when the second train catches up with the first train, we can set up the following equation:

40t = 50(t-1)

Let's solve this equation:

40t = 50t - 50

10t = 50

t = 5

Therefore, the second train will catch up with the first train after 5 hours.

Now, let's calculate the distance traveled by each train during that time:

Distance traveled by the first train = 40 * t = 40 * 5 = 200 miles

Distance traveled by the second train = 50 * (t-1) = 50 * (5-1) = 50 * 4 = 200 miles

Therefore, both trains would have traveled 200 miles by the time the second train catches up with the first train.